Fuzzy Order Convergence of Double Sequences in Fuzzy Riesz Spaces

في هذا البحث قدمنا بعض المفاهيم حول التقارب الرتيب الضبابي للمتتاليات المزدوجة في فضاءات ريسز الضبابية, وكذلك عرفنا نوع جديد من التقارب وهو تقارب   وتقارب كوشي  للمتتاليات المزدوجة في فضاء ريسز الضبابي , ومن ثم برهنا بعض النتائج المهمة التي تتعلق في هذه المفاهيم.      In this paper, we introduce the concepts of fuzzy order convergence of double sequence, also define a new type of convergence, that is,  Convergence and  Cauchy of double sequence in fuzzy Riesz space and then prove some interesting results related to these notions.   &nbsp

LIFE AND WORK OF DOMENICO CANDELORO: AN APPRECIATION

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ON f−LACUNARY STATISTICAL CONVERGENCE OF ORDER β OF DOUBLE SEQUENCES FOR DIFFERENCE SEQUENCES OF FRACTIONAL ORDER

In this study, by using definition of lacunary statistical convergence we introduce the concepts of f− lacunary statistical convergence of order β and strongly f−lacunary summability of order β of double sequences for different sequences of fractional order spaces. Also, we establish some inclusion relations between these concepts

On the coexistence of position and momentum observables

We investigate the problem of coexistence of position and momentum observables. We characterize those pairs of position and momentum observables which have a joint observable

Stieltjes-Type Integrals for Metric Semigroup-Valued Functions Defined on Unbounded Intervals

Abstract We introduce the GH k integral for functions defined on (possibly) unbounded subintervals of the extended real line and with values in metric semigroups. Basic properties and convergence theorems for this integral are deduced

Statistically multiplicative convergence on locally solid Riesz algebras

In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to the algebra multiplication and the solid topology. We study on this concept and we give the notion of $\mathbb{st_m}$-bounded sequence, and also, we prove some relations between this convergence and the other convergences such as the order convergence and the statistical convergence in topological spaces. Also, we give some results related to semiprime $f$-algebras.Comment: 15 Page

MATRIX TRANSFORMS OF SPEED-SUMMABLE AND SPEED-BOUNDED SEQUENCES

First we recall the notions of $A^{\lambda}$-boundedness, $A^{\lambda}$-summability and the absolute $A^{\lambda}$-summability of sequences, and the notion of $\lambda$-reversibility of $A$, where $A$ is a matrix with real or complex entries and $\lambda$ is the speed of convergence, \ie; a monotonically increasing positive sequence. Let $B$ be a lower triangular matrix with real or complex entries, and $\mu=(\mu_{n})$ be another speed of convergence. We find necessary and sufficient conditions for a matrix $M$ (with real or complex entries) to map the set of all $A^{\lambda}$-bounded sequences (for a normal matrix $A$) into the set of all absolutely $B^{\mu}$-summable sequences, and the set of all $A^{\lambda}$-summable sequences (for a $\lambda$-reversible matrix $A$) into the set of all absolutely $B^{\mu}$-summable sequences